Problem 57 - Precalculus Essentials

Question

Find a positive angle less than \(360^{\circ}\) or \(2 \pi\) that is coterminal with the given angle. $$395^{\circ}$$

Step-by-Step Solution

Answer

The positive angle less than \(360^{\circ}\) that is coterminal with \(395^{\circ}\) is \(35^{\circ}\).

Step 1: Understand the Problem

The problem asks to find a positive angle which is less than \(360^{\circ}\) or \(2 \pi\) radians and is coterminal with \(395^{\circ}\). This requires understanding what coterminal angles are. Two angles are coterminal if they have the same initial side and terminal side.

Step 2: Identify the Increment

In order to find an angle coterminal to \(395^{\circ}\) that is less than \(360^{\circ}\), first identify the increment that separates equivalent angle measurements. In this case, every full rotation of \(360^{\circ}\) brings us back to the same position.

Step 3: Subtract the Increment

Subtract the increment identified in Step 2 from the given angle until a measurement less than \(360^{\circ}\) is reached. In this case, \(395^{\circ} - 360^{\circ} = 35^{\circ}\). Therefore, \(35^{\circ}\) is an angle that is coterminal with \(395^{\circ}\) and is less than \(360^{\circ}\).